Question

February 12, 2009 marked the 200 ^th anniversary of Charles Darwin's birth. To celebrate, Gallup, a national polling organization, surveyed 1,018 randomly selected American adults about their education level and their beliefs about the theory of evolution. In their sample, 325 of their respondents had some college education and 228 were college graduates. Among the 325 respondents with some college education, 133 said that they believed in the theory of evolution. Among the 228 respondents who were college graduates, 121 said that they believed in the theory of evolution.

a) Construct a 90% confidence interval for the difference between the proportions of college graduates and individuals with some college who believe in the theory of evolution. Round your sample proportions and margin of error to three decimal places.

b) Test, at the 10% level, if there is evidence that the proportion of college graduates that believe in evolution differs significantly from the proportion of individuals with some college education that believe in evolution. Include all of the details of the test.

c) Verify that the sample size is large enough in each group to use the normal distribution to construct a confidence interval for a difference in proportions.

Answer 1